If D0 is the outer diameter of the coil and Di is the inner diameter of the coil

Question

If D0 is the outer diameter of the coil and Di is the inner diameter of the coil, and t=0.14cm is the thickness of the wire, find the number of layers within the solenoid..So i'm unsure of how to compute this? Also the Magnetic field equation what does the variable w stand for?

If X1 is the perpendicular distance from the current segment to the pivot point, the torque about the pivot point due to the magnetic force is tau B = FX1 = Ib Lb BX1 This torque will be balanced by the gravity force acting on small wire weights added to the other end of the current balance. If n wire weights are put on the other end at distance X2 from the pivot point, the torque due to gravity is tau g = nwX2 To balance, the two torques must be equal in magnitude: IbLbBX1 = nwX2 so the magnitude of the magnetic field B can be calculated:

Explanation / Answer

this can be done using torque balance equation ::

F = force due to magnetic field on current carrying wire

= I*L*B

where I = current , L = length of wire

TB = Torque due to force F   = F*X1 = I*L*B *X1

let W = wieght of signle wire = mg

W1 = weight of n wires = n*mg = nW

TW = Tqorque due to weight =W1*X2   =   nWX2

balancing Torque :: TB = Tw

                             

                         I*L*B *X1   = nWX2

                                B = nWX2/(I*L*X1)

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